User:BudjarnLambeth/Hem: Difference between revisions

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Noticed the wiki doesn't have a page on hem yet, so copy pasting Scott Dakota's explanation of it on this user page so that I or someone else can reference this and write a proper main space page on it later.
 
BudjarnLambeth (talk | contribs)
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m Replaced content with "See Barton."
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'''Noticed the wiki doesn't have a page on hem yet, so copy pasting [[Scott Dakota]]'s explanation of it on this user page so that I or someone else can reference this and write a proper main space page on it later.'''
See [[Barton]].
 
 
<pre>
Struck gold in the GS investigation of 37ed2 project:
 
(11/8)^3 ~= 13/5
via 6656/6655, a very tight microtemperament comma, 0.26c. This feels like the inner sanctum secret trick inside 37ed2.
 
Then found the second trick!
(13/10)^2 ~= 22/13, via 2200/2197.
 
Putting this all together in 2.5.11.13, this means that if we stack prime 11 a lot, we also get a huge amount of ~ 13/10 and 13/11 and 11/10 and 55/32 for free as well.
 
The GS tweaks required to make these analogies overt are very small. Microtemperament grade tweaks. I'm amazed at how Platonic-ideal archetypal this GS is. This is perhaps the best no-prime-3 GS territory I've come across so far, because such low error and such a high proportion of concordant chords in the rendered scales.
 
Hem GS:
GS(11 11 13/605 11 5/1859 11 11 13/605) aka
GS(11/8 11/8 832/605
11/8 2560/1859
11/8 11/8 832/605)
gg: (88/5)^(1/9) 551.667c
interval of duplication: 11/10
CS: 5 7 9 11 13 24 37
50 87 124 211 298 385 472 559  etc.
 
Hem[37] is a super smooth rational detemper of 37ed2, and Hem[11] and [13] are also extremely well distributed and musical.
 
For xenners into exploring no-prime-3 land but still into having a lot of alternative concordant chords on hand, this territory is about as good as it gets.
 
https://scaleworkshop.plainsound.org/scale/iestQHpCn
 
Hem[11]
 
this is such a badass no-3's JI scale, remarkable
 
https://scaleworkshop.plainsound.org/scale/jesgMz7oe
 
Hem[13]
 
equally badass cool
 
https://scaleworkshop.plainsound.org/scale/jesV_Vb0i
 
FYI the name Hem is a riff on Emka 24 & 37 temperament in 2.5.11.13 or 2.5.7.11.13, which leverages <6656/6655, 2200/2197>
---
this all seems to be the key to 37ed2's magic
 
-- Scott Dakota
</pre>

Latest revision as of 04:28, 2 October 2025

See Barton.

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